Simulation of multiple morphogenetic movements in the Drosophila embryo by a single 3D finite element model

The present work describes a 3D finite element model of the Drosophila embryo designed to simulate three morphogenetic movements during early gastrulation: ventral furrow invagination, cephalic furrow formation and germ band extension. The embryo is represented by a regular ellipsoid and only the mesoderm is modeled. Additionally, the parametric description of the biological structure in a special curvilinear system provides mesh-independent endogenous strains. A deformation gradient decomposition is used to couple an active deformation, specific for each morphogenetic movement, together with a passive deformation, which is due to the response of the continuous mesoderm. Boundary conditions such as the rigid contact with the external vitelline membrane and the yolk pressure are also taken into account. The results suggest that the number of active strains responsible for the morphogenetic events can be less than that deduced from direct experimental observations. Finally, the estimation of the non-local pressures induced during morphogenetic movements is in good agreement with the experimental data.